ALow-order Model of Two-dimensional Fluid Dynamics on the Surface of a Sphere

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土性平稳随机场的空间统计特性分析

阐明了平稳随机场的空间统计特性,根据平稳随机场各态历经性概念,讨论了土层满足各态历经性的条件,以及计算空间平均方差和相关距离的公式。并结合工程实例,分析了空间平均方差计算的影响因素。     

海洋地基土的随机场特性

对随机场理论应用于海洋土地基可靠度研究中的必要性及其理论意义进行了深入的分析和探讨，提出了检验土性指标的平稳性和各态历经性的方法，结合渤海油田在开发和建设中积累的大量工程地质勘察资料，对海洋土竖直和水平向土性剖面建立齐次正态随机场模型。并在此基础上，以渤海某油田海洋平台的地基可靠度分析为例，说明随机场理论在海洋土地基可靠度分析中的具体应用及其所发挥的重要作用。     

Application of Random Process in Soil Profile Modeling

When using the random process in soil profile modeling, the stationary and ergodicity of thesoil properties in the profile must be tested. This paper describes a procedure for stationary and ergodicity testing. Numerical examples were given for demonstration. A log-cosine function is suggested to simulate the correlation function, which has been proved to be good for soil profile modeling.     

Non‐ergodicity and PEER's framework formula

A framework formula for performance‐based earthquake engineering, advocated and used by researchers at the Pacific Earthquake Engineering Research (PEER) Center, is closely examined. The formula was originally intended for computing the mean annual rate of a performance measure exceeding a specified threshold. However, it has also been used for computing the probability that a performance measure will exceed a specified threshold during a given period of time. It is shown that the use of the formula to compute such probabilities could lead to errors when non‐ergodic variables (aleatory or epistemic) are present. Assuming a Poisson model for the occurrence of earthquakes in time, an exact expression is derived for the probability distribution of the maximum of a performance measure over a given period of time, properly accounting for non‐ergodic uncertainties. This result is used to assess the approximation involved in the PEER formula for computing probabilities. It is found that the PEER approximation of the probability has a negligible error for probabilities less than about 0.01. For larger probabilities, the error depends on the magnitude of non‐ergodic uncertainties and the duration of time considered and can be as much as 20% for probabilities around 0.05 and 30% for probabilities around 0.10. The error is always on the conservative side. Copyright © 2005 John Wiley & Sons, Ltd.     

The deterministic side of geostatistics

The probabilistic approach is but one language used by geostatisticians to characterize spatial variability and to express a very simple criterion for goodness of estimation. Notions such as stationarity and ergodicity are important for the consistency of the probabilistic language but are irrelevant to the real problem, that of estimating a well-defined deterministic spatial average. The kriging algorithm is established without any recourse to probabilistic modeling or notation.     

Ergodicity and the ‘scale effect’

Solute plume spreading in an aquifer exhibits a ‘scale effect’ if the second spatial concentration moment of a plume has a non-constant time-derivative. Stochastic approaches to modeling this scale effect often rely on the critical assumption that ensemble averages can be equated to spatial averages measured in a single field experiment. This ergodicity assumption should properly be evaluated in a strictly dynamical context, and this is done in the present paper. For the important case of trace plume convection by steady groundwater flow in an isotropic, heterogeneous aquifer, ergodicity does not obtain because of the existence of an invariant function on stream surfaces that is not uniform throughout the aquifer. The implications of this result for stochastic models of solute transport are discussed. © 1997 Elsevier Science Ltd. All rights reserved     

Kriging in a finite domain

Adopting a random function model {Z(u),u study areaA} and using the normal equations (kriging) for estimation amounts to assume that the study areaA is embedded within a infinite domain. At first glance, this assumption has no inherent limitations since all locations outsideA are of no interest and simply not considered. However, there is an interesting and practically important consequence that is reflected in the kriging weights assigned to data contiguously aligned along finite strings; the weights assigned to the end points of a string are large since the end points inform the infinite half-space beyond the string. These large weights are inappropriate when the finite string has been created by either stratigraphic/geological limits or a finite search neighborhood. This problem will be demonstrated with numerical examples and some partial solutions will be proposed.     

关于固体地球系统与地质作用的三点认识

文中讨论了作为极复杂巨系统的固体地球内部运动规律的 3条推论 :(1)地球系统在偏离平衡态时 ,有选择能量耗散最小方式的“惯性” ,在系统内禀熵急增时或者回到一种准稳定的定态 ,或者通过自组织迅速减少内禀熵增加率。换言之 ,地球系统可能有种尽量保存自身内能不受大量耗散的惯性 ,使其总体内禀熵产生率对时空的积分取极小值。我们把这一认识称为总体熵产生率取极小准则 ,对于孤立与渐变的地质过程 ,它等同于热力学第二定律与普里高津最小熵产生原理 ,对于极复杂地球巨系统及远离平衡态情况加了“总体”两字 ,意思是在局部或短期突变时熵产生率可能是大的 ,但它对全球与长时间的积分而言仍然取极小。换句话说 ,作为一个巨系统 ,固体地球在其局部远离平衡状态时 ,仍然能保持总体上内能消耗取极小的惯性 ,维持对全部固体地球时空系统总体熵产生率取极小准则。 (2 )关于地质作用过程演化的定态遍历准则。地球系统的复杂性不仅表现在其非线性 ,即同时存在着多种可能的定态作为其演化的趋势 ,而且表现在其时空发展过程中将经历尽可能多的定态。非线性非平衡态动力学的一般规律符合大多数包含激变事件的地质作用过程。将来在地球系统偏离平衡态足够远时 ,它可能会具有无穷多个耗散结构 ,因而使系统进入完全?